Time-reversion is a well known technique that is used in time series analysis since Box and Jenkins (1970) proposed to compute unconditional least-squares estimations by backcasting. However, in a multivariate setting its application relies on a state space formulation of the time series model and the use of some results about reversion in time of Markov processes. Given a VARMA process, this paper proposes a new polynomial methodology that can be used to provide a model for the timereversed process. A simple example is provided and some possible applications and extensions are also included.

Keywords: VARMA, time-reversion, echelon form, backcasting.